# -*- coding: utf-8 -*-
#
import numpy


class XiaoGimbutas(object):
    '''
    Hong Xiao, Zydrunas Gimbutas,
    A numerical algorithm for the construction of efficient quadrature rules in
    two and higher dimensions,
    Computers & Mathematics with Applications,
    Volume 59, Issue 2, January 2010, Pages 663–676,
    <https://doi.org/10.1016/j.camwa.2009.10.027>.

    Abstract:
    We present a numerical algorithm for the construction of efficient,
    high-order quadratures in two and higher dimensions. Quadrature rules
    constructed via this algorithm possess positive weights and interior nodes,
    resembling the Gaussian quadratures in one dimension. In addition, rules
    can be generated with varying degrees of symmetry, adaptable to individual
    domains. We illustrate the performance of our method with numerical
    examples, and report quadrature rules for polynomials on triangles,
    squares, and cubes, up to degree 50. These formulae are near optimal in the
    number of nodes used, and many of them appear to be new.

    Data adapted from
    <https://people.sc.fsu.edu/~jburkardt/f_src/triangle_symq_rule/triangle_symq_rule.f90>.
    '''
    def __init__(self, index):
        # True most of the time, but overridden for some indices.
        self.degree = index

        if index == 1:
            bary = numpy.array([
                [
                    0.25, 0.25,
                    0.25, 0.25,
                ],
                ])
            self.weights = numpy.array([
                1.0,
                ])
        elif index == 2:
            bary = numpy.array([
                [
                    0.365314518814635, 0.180029693510365,
                    0.00692323557362747, 0.447732552101373,
                ],
                [
                    0.457461587085596, 0.155933120499186,
                    0.381765356069347, 0.0048399363458718,
                ],
                [
                    0.000375515028729282, 0.216076429184848,
                    0.430701707077836, 0.352846348708587,
                ],
                [
                    0.123666800328458, 0.82157254096762,
                    0.0399330486414984, 0.0148276100624234,
                ],
                ])
            self.weights = numpy.array([
                0.300520939336976,
                0.278777576686568,
                0.319093935501475,
                0.101607548474981,
                ])
        elif index == 3:
            bary = numpy.array([
                [
                    0.439858947649275, 0.190117002439284,
                    0.0114033294445572, 0.358620720466884,
                ],
                [
                    0.124804862165247, 0.158685163227441,
                    0.585662805655216, 0.130847168952096,
                ],
                [
                    0.345444155719731, 0.0109052122111892,
                    0.281523802123546, 0.362126829945534,
                ],
                [
                    0.141482751969504, 0.571226052149115,
                    0.14691839008717, 0.140372805794211,
                ],
                [
                    0.037871631782357, 0.170816925164989,
                    0.152818143090927, 0.638493299961727,
                ],
                [
                    0.641429791495696, 0.162001491698524,
                    0.183850350492098, 0.0127183663136814,
                ],
                ])
            self.weights = numpy.array([
                0.132568027144445,
                0.224415166917557,
                0.128066412710747,
                0.252003980809502,
                0.140624409660403,
                0.122322002757345,
                ])
        elif index == 4:
            bary = numpy.array([
                [
                    0.106604172561994, 0.0972046445875833,
                    0.68439041545304, 0.111800767397383,
                ],
                [
                    0.329232959742647, 0.0295694952064796,
                    0.317903560213395, 0.323293984837479,
                ],
                [
                    0.103844116410993, 0.432710239047769,
                    0.353823239209297, 0.109622405331941,
                ],
                [
                    0.304448402434497, 0.240276664928073,
                    0.126801725915392, 0.328473206722038,
                ],
                [
                    0.538007203916186, 0.12941137378891,
                    0.330190414837464, 0.00239100745743937,
                ],
                [
                    0.00899126009333578, 0.121541991333928,
                    0.30649398842969, 0.562972760143046,
                ],
                [
                    0.432953490481356, 0.450765876091277,
                    0.0594566162994338, 0.0568240171279337,
                ],
                [
                    0.0533412395357452, 0.419266313879513,
                    0.0477814355590867, 0.479611011025655,
                ],
                [
                    0.741228882093623, 0.0672232948933834,
                    0.0351839297735987, 0.156363893239395,
                ],
                [
                    0.0814049184028593, 0.752508507009655,
                    0.0680993709382067, 0.0979872036492791,
                ],
                [
                    0.174694058697231, 0.0404905067275904,
                    0.0135607018798029, 0.771254732695376,
                ],
                ])
            self.weights = numpy.array([
                0.10646803415549,
                0.110234232428498,
                0.154976116016246,
                0.193410812049634,
                0.0761627152455584,
                0.0794266800680253,
                0.0694699659376354,
                0.0599331851465595,
                0.0553937988715764,
                0.0552733691559369,
                0.03925109092484,
                ])
        elif index == 5:
            bary = numpy.array([
                [
                    0.0927352503108913, 0.0927352503108913,
                    0.721794249067326, 0.0927352503108911,
                ],
                [
                    0.0455037041256497, 0.45449629587435,
                    0.45449629587435, 0.0455037041256496,
                ],
                [
                    0.45449629587435, 0.0455037041256497,
                    0.45449629587435, 0.0455037041256497,
                ],
                [
                    0.0455037041256497, 0.0455037041256497,
                    0.45449629587435, 0.45449629587435,
                ],
                [
                    0.310885919263301, 0.310885919263301,
                    0.0673422422100981, 0.310885919263301,
                ],
                [
                    0.310885919263301, 0.0673422422100983,
                    0.310885919263301, 0.3108859192633,
                ],
                [
                    0.0673422422100983, 0.310885919263301,
                    0.310885919263301, 0.310885919263301,
                ],
                [
                    0.310885919263301, 0.310885919263301,
                    0.310885919263301, 0.067342242210098,
                ],
                [
                    0.0927352503108913, 0.721794249067326,
                    0.0927352503108912, 0.0927352503108913,
                ],
                [
                    0.0927352503108913, 0.0927352503108911,
                    0.0927352503108913, 0.721794249067326,
                ],
                [
                    0.721794249067326, 0.0927352503108912,
                    0.0927352503108913, 0.0927352503108913,
                ],
                [
                    0.45449629587435, 0.45449629587435,
                    0.0455037041256496, 0.0455037041256497,
                ],
                [
                    0.0455037041256497, 0.45449629587435,
                    0.0455037041256497, 0.45449629587435,
                ],
                [
                    0.45449629587435, 0.0455037041256497,
                    0.0455037041256496, 0.45449629587435,
                ],
                ])
            self.weights = numpy.array([
                0.073493043116362,
                0.0425460207770815,
                0.0425460207770815,
                0.0425460207770815,
                0.112687925718016,
                0.112687925718016,
                0.112687925718016,
                0.112687925718016,
                0.0734930431163619,
                0.0734930431163619,
                0.0734930431163619,
                0.0425460207770814,
                0.0425460207770815,
                0.0425460207770815,
                ])
        elif index == 6:
            bary = numpy.array([
                [
                    0.0243189742481429, 0.0388360843448845,
                    0.902928799013611, 0.0339161423933614,
                ],
                [
                    0.267844198183576, 0.0647694369300529,
                    0.636767508558514, 0.0306188563278576,
                ],
                [
                    0.0234677955730546, 0.0647751604471051,
                    0.390862050671012, 0.520894993308829,
                ],
                [
                    0.0637328952949977, 0.277903669330078,
                    0.594909689021796, 0.0634537463531287,
                ],
                [
                    0.0836788140600551, 0.0660986624146805,
                    0.63005455511099, 0.220167968414275,
                ],
                [
                    0.329379718549198, 0.325119658577025,
                    0.326833504619046, 0.0186671182547306,
                ],
                [
                    0.304169265349782, 0.319194280348931,
                    0.0443833443572082, 0.332253109944079,
                ],
                [
                    0.038288670738245, 0.328388171231222,
                    0.320287433697693, 0.313035724332841,
                ],
                [
                    0.351939197334705, 0.0550990224907257,
                    0.38108430890631, 0.21187747126826,
                ],
                [
                    0.152103811309931, 0.124649963637486,
                    0.201234567364421, 0.522011657688162,
                ],
                [
                    0.624321363553429, 0.0659249231600099,
                    0.2535936747432, 0.0561600385433603,
                ],
                [
                    0.211297658581586, 0.00735452383806937,
                    0.25118449527753, 0.530163322302815,
                ],
                [
                    0.0631999809425695, 0.617455720147269,
                    0.258449148983926, 0.0608951499262361,
                ],
                [
                    0.255820784264986, 0.279420052945988,
                    0.269569929633272, 0.195189233155754,
                ],
                [
                    0.577345781389727, 0.287725094826464,
                    0.0646206380733685, 0.0703084857104406,
                ],
                [
                    0.0651779927633704, 0.594717301875796,
                    0.0666032980076031, 0.273501407353231,
                ],
                [
                    0.530063275481017, 0.0667895997817381,
                    0.0769927171009672, 0.326154407636278,
                ],
                [
                    0.248449540118895, 0.626540201708882,
                    0.0621155331835988, 0.0628947249886239,
                ],
                [
                    0.213041183236186, 0.0600105830202691,
                    0.0258426862607033, 0.701105547482842,
                ],
                [
                    0.0539961408359145, 0.275786300469851,
                    0.0600161491661687, 0.610201409528066,
                ],
                [
                    0.841138951662318, 0.0513252061652029,
                    0.0372647521383555, 0.0702710900341231,
                ],
                [
                    0.0087819577775189, 0.0405760510668179,
                    0.0886003504689102, 0.862041640686753,
                ],
                [
                    0.0228658238140231, 0.903770001332182,
                    0.0293357210831787, 0.0440284537706163,
                ],
                ])
            self.weights = numpy.array([
                0.00709579485165953,
                0.0315094098827064,
                0.0242312868774444,
                0.0488900759024422,
                0.0530333239081694,
                0.0432392966954734,
                0.067135816212557,
                0.0598213476614292,
                0.0626144752813113,
                0.0643340219730875,
                0.0435903980606292,
                0.0225656672781428,
                0.0466131341265807,
                0.112599404494068,
                0.053935010628312,
                0.0497686300915143,
                0.0630663618855205,
                0.0471480304722612,
                0.0255043242670424,
                0.0397140976490823,
                0.0159254791850038,
                0.0104233357236959,
                0.00724127689186697,
                ])
        elif index == 7:
            bary = numpy.array([
                [
                    0.00199682581829981, 0.0192079934885854,
                    0.651334895848238, 0.327460284844877,
                ],
                [
                    0.0609221845854508, 0.323456841789598,
                    0.61517098831187, 0.000449985313081031,
                ],
                [
                    0.063969430325799, 0.0624740225231503,
                    0.812872555571, 0.0606839915800507,
                ],
                [
                    0.23078490023767, 0.0140330844733053,
                    0.566163074530697, 0.189018940758327,
                ],
                [
                    0.323948070989182, 0.0624444127129091,
                    0.586321285830122, 0.0272862304677867,
                ],
                [
                    0.350115304507171, 0.261508769176583,
                    0.0119758768891576, 0.376400049427089,
                ],
                [
                    0.022532983493832, 0.260420587998262,
                    0.564650102467691, 0.152396326040215,
                ],
                [
                    0.500378669849815, 0.258280547367444,
                    0.0826690956073921, 0.158671687175349,
                ],
                [
                    0.289861281908691, 0.397174402994917,
                    0.171048877818779, 0.141915437277613,
                ],
                [
                    0.157241855986003, 0.55045594162486,
                    0.0437434701607319, 0.248558732228405,
                ],
                [
                    0.631548473918005, 0.0258331677317304,
                    0.280405238101906, 0.062213120248359,
                ],
                [
                    0.111251133426943, 0.107462430783153,
                    0.475849161739315, 0.305437274050589,
                ],
                [
                    0.217554444216353, 0.252130530629395,
                    0.448739255383575, 0.0815757697706759,
                ],
                [
                    0.0446302679066366, 0.601823577631812,
                    0.289994034365513, 0.0635521200960386,
                ],
                [
                    0.0762414702839689, 0.0331656998310357,
                    0.274801534897994, 0.615791294987002,
                ],
                [
                    0.437248089764549, 0.109895976327021,
                    0.276571682738858, 0.176284251169573,
                ],
                [
                    0.0740087021391158, 0.41035809599494,
                    0.244761650919342, 0.270871550946603,
                ],
                [
                    0.218812622547504, 0.176438223014948,
                    0.175766110266451, 0.428983044171096,
                ],
                [
                    0.00161353261999009, 0.199110572052883,
                    0.263747375338565, 0.535528519988562,
                ],
                [
                    0.234396497335962, 0.528711306413653,
                    0.216998299345866, 0.0198938969045188,
                ],
                [
                    0.350528406837283, 0.00392965148708786,
                    0.241844613058583, 0.403697328617046,
                ],
                [
                    0.550888978142213, 0.223470202530143,
                    0.225528537697264, 0.000112281630380141,
                ],
                [
                    0.0680111048992614, 0.297785234383524,
                    0.0476494431008923, 0.586554217616322,
                ],
                [
                    0.627983229358597, 0.293770036523707,
                    0.0274823781928344, 0.0507643559248611,
                ],
                [
                    0.599019239879897, 0.0528776293788545,
                    0.0549795828955141, 0.293123547845734,
                ],
                [
                    0.275309810687132, 0.0530001383345468,
                    0.0449776631268801, 0.626712387851441,
                ],
                [
                    0.319658376097012, 0.599100943620026,
                    0.0352137952974546, 0.0460268849855079,
                ],
                [
                    0.062815072845237, 0.820745300741595,
                    0.0589104128256091, 0.057529213587559,
                ],
                [
                    0.824544066695395, 0.0598941950699869,
                    0.0567758666899469, 0.0587858715446707,
                ],
                [
                    0.0521366890580109, 0.0620110919366441,
                    0.0571821545167788, 0.828670064488566,
                ],
                [
                    0.000500433444271841, 0.635521510583761,
                    0.0598944722319085, 0.304083583740058,
                ],
                ])
            self.weights = numpy.array([
                0.00770818116200049,
                0.0120037921882199,
                0.0232168093278622,
                0.0224113653953913,
                0.0232909869573198,
                0.0273299143176464,
                0.0287962835952346,
                0.0429911619639807,
                0.0527816656535537,
                0.0418385316076004,
                0.0207120821637628,
                0.0603015155912097,
                0.0667112071657317,
                0.0314111274554996,
                0.0283127876119325,
                0.0667394894208807,
                0.0641888389354599,
                0.0823381687805698,
                0.0208727051617902,
                0.0245624298859732,
                0.0223486714825842,
                0.0221803191752118,
                0.0369358091114385,
                0.0167020010636449,
                0.033795865302751,
                0.0280611783139331,
                0.0210927658418785,
                0.0205903486322805,
                0.0192028117961788,
                0.0180570774841578,
                0.0125141074543206,
                ])
        elif index == 8:
            bary = numpy.array([
                [
                    0.0176071561268785, 0.00885559427870577,
                    0.948563929799005, 0.024973319795411,
                ],
                [
                    0.189074468870033, 0.0362046719285183,
                    0.731367360036089, 0.043353499165359,
                ],
                [
                    0.230743496794649, 0.611336533691884,
                    0.00557577303043824, 0.152344196483028,
                ],
                [
                    0.0258068488725323, 0.0277767579935654,
                    0.466540585890919, 0.479875807242983,
                ],
                [
                    0.0464861294110928, 0.156486685040066,
                    0.751496536151838, 0.0455306493970033,
                ],
                [
                    0.249637083057875, 0.195546081922602,
                    0.541793182461809, 0.013023652557713,
                ],
                [
                    0.0490853443274963, 0.0414941590182784,
                    0.71717735709395, 0.192243139560275,
                ],
                [
                    0.257916673154309, 0.220977464998818,
                    0.0123959233601955, 0.508709938486678,
                ],
                [
                    0.0431223833778798, 0.415076584269989,
                    0.494799169319991, 0.0470018630321401,
                ],
                [
                    0.199906729032922, 0.479406653352866,
                    0.320095606750398, 0.000591010863814574,
                ],
                [
                    0.123978489327818, 0.0622443994610205,
                    0.403654775010059, 0.410122336201102,
                ],
                [
                    0.0338367380972239, 0.212519226117529,
                    0.50564195098037, 0.248002084804877,
                ],
                [
                    0.382880501165727, 0.397275457461443,
                    0.0817336282047911, 0.138110413168039,
                ],
                [
                    0.472133219549673, 0.0454473742628588,
                    0.435666994545663, 0.0467524116418051,
                ],
                [
                    0.49359008083402, 0.216139692630079,
                    0.0391905731975356, 0.251079653338365,
                ],
                [
                    0.250227446293038, 0.0452907498885836,
                    0.493144767959065, 0.211337035859313,
                ],
                [
                    0.182246049223361, 0.428407770736019,
                    0.0619469615468447, 0.327399218493776,
                ],
                [
                    0.228080184055079, 0.142514629908895,
                    0.128143739766618, 0.501261446269409,
                ],
                [
                    0.0308224720999311, 0.181262191170945,
                    0.25934638915961, 0.528568947569513,
                ],
                [
                    0.164695505900328, 0.249520766079952,
                    0.249905550725755, 0.335878177293964,
                ],
                [
                    0.0424303011456228, 0.48622524586616,
                    0.275236027299907, 0.196108425688311,
                ],
                [
                    0.200330706877803, 0.227462049986755,
                    0.448954528663698, 0.123252714471744,
                ],
                [
                    0.411896203648412, 0.15825909334589,
                    0.207391735140623, 0.222452967865074,
                ],
                [
                    0.511106071913577, 0.0288272589009354,
                    0.229540713072656, 0.230525956112832,
                ],
                [
                    0.48351828029101, 0.229540615063575,
                    0.24201755731748, 0.0449235473279347,
                ],
                [
                    0.209642302870646, 0.485313557638069,
                    0.198619977669231, 0.106424161822054,
                ],
                [
                    0.250471921917321, 0.0226109096366605,
                    0.222434642492779, 0.50448252595324,
                ],
                [
                    0.0367806497347482, 0.720511165717872,
                    0.204368923907325, 0.0383392606400548,
                ],
                [
                    0.461811725168263, 0.465315160413036,
                    0.00542218330717809, 0.0674509311115227,
                ],
                [
                    0.0504550069317247, 0.0393802186845056,
                    0.173195608683351, 0.736969165700418,
                ],
                [
                    0.748574560745763, 0.0454345303521096,
                    0.163299343299354, 0.0426915656027734,
                ],
                [
                    0.0309505292161329, 0.424650054079589,
                    0.136206241225198, 0.40819317547908,
                ],
                [
                    0.0543830156062334, 0.216264148890651,
                    0.0512537651338738, 0.678099070369241,
                ],
                [
                    0.70165677606439, 0.204491813747223,
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            self.weights = numpy.array([
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                [
                    0.391993350183357, 0.191418178100784,
                    0.0306082825277231, 0.385980189188136,
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                    0.191418178100992, 0.385980189186922,
                    0.0306082825276405, 0.391993350184446,
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                [
                    0.547935626185202, 0.0679470990326355,
                    0.303613592364941, 0.0805036824172211,
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                    0.0679470990322547, 0.0805036824168604,
                    0.303613592365006, 0.547935626185879,
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                    0.0805036824174764, 0.547935626184953,
                    0.303613592364535, 0.0679470990330357,
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                [
                    0.153806036080323, 0.332296083385487,
                    0.164432709777014, 0.349465170757176,
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                [
                    0.332296083385749, 0.349465170756816,
                    0.164432709777204, 0.15380603608023,
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                [
                    0.34946517075658, 0.153806036080343,
                    0.164432709777114, 0.332296083385963,
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                [
                    0.680146917763508, 0.101517159170244,
                    0.116272488104425, 0.102063434961823,
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                    0.101517159169978, 0.102063434961844,
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                    0.11627248810427, 0.101517159170411,
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                [
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                [
                    0.104034774509461, 0.287422475829685,
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                    0.287422475830375, 0.00560141769466357,
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                [
                    0.212942537144676, 0.0212807476383709,
                    0.743707421058246, 0.0220692941587074,
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                [
                    0.0212807476385626, 0.0220692941588891,
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                [
                    0.923299965157474, 0.0132755319408302,
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                [
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                [
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                [
                    0.526455163784847, 0.00323980932993712,
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                [
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                [
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                ])
            self.weights = numpy.array([
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                0.00262094309420437,
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                0.00262094309421372,
                0.00314384255747847,
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                0.000306242271791608,
                0.00944673970204934,
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                0.00944673970206581,
                0.010075594148571,
                0.0100755941485464,
                0.0100755941485896,
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                0.0179006739481154,
                0.0179006739481161,
                0.0100585702279102,
                0.0100585702279099,
                0.0100585702279198,
                0.00309502298940197,
                0.00309502298938067,
                0.00309502298936173,
                0.0028684551031174,
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                0.002868455103146,
                0.000386552336917729,
                0.000386552336931858,
                0.000386552336897364,
                0.00225666323399646,
                0.00225666323407603,
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                ])
        else:
            assert index == 15
            self.degree = 16
            bary = numpy.array([
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                    0.402153395912455, 0.267805847317026,
                    0.320387028932337, 0.00965372783818291,
                ],
                [
                    0.267805847317044, 0.00965372783817742,
                    0.320387028932318, 0.40215339591246,
                ],
                [
                    0.00965372783817779, 0.402153395912491,
                    0.320387028932303, 0.267805847317029,
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                    0.477411856648227, 0.267326785868425,
                    0.162728234374927, 0.0925331231084208,
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                    0.267326785868413, 0.0925331231083885,
                    0.162728234374953, 0.477411856648245,
                ],
                [
                    0.0925331231084195, 0.477411856648248,
                    0.162728234374932, 0.2673267858684,
                ],
                [
                    0.208457799408109, 0.255795941906351,
                    0.0113344782305252, 0.524411780455015,
                ],
                [
                    0.255795941906343, 0.52441178045503,
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                ],
                [
                    0.524411780455004, 0.208457799408117,
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                    0.704703873882076, 0.0731393403677198,
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                    0.0151184354245824, 0.0476594460606897,
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                ],
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                [
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                    0.0116727591178493, 0.0103499066006764,
                ],
                [
                    0.235285750794233, 0.0103499066006743,
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                ],
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                    0.0103499066006717, 0.742691583487255,
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                [
                    0.52497718614148, 0.0136722640125399,
                    0.0102920818969296, 0.451058467949051,
                ],
                [
                    0.185669571420531, 0.00940743474102812,
                    0.498715106027506, 0.306207887810935,
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                [
                    0.00940743474103265, 0.306207887810909,
                    0.49871510602753, 0.185669571420529,
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                    0.306207887810928, 0.185669571420529,
                    0.498715106027514, 0.00940743474102935,
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                ],
                [
                    0.0133390399676393, 0.3718583817617,
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                ],
                [
                    0.00884804648943756, 0.0290441392868168,
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                    0.770601840442029, 0.0148809324152256,
                    0.145750781988841, 0.0687664451539042,
                ],
                [
                    0.0148809324152255, 0.0687664451539022,
                    0.145750781988846, 0.770601840442026,
                ],
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                ],
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                ],
                [
                    0.378974507003849, 0.225555068788825,
                    0.0126442918856677, 0.382826132321658,
                ],
                [
                    0.175288263255126, 0.333784772736308,
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                [
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                    0.153656889862301, 0.175288263255125,
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                [
                    0.337270074146239, 0.175288263255117,
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                ],
                [
                    0.0160230796339641, 0.423660805665255,
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                ],
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                    0.370614454518771, 0.0160230796339625,
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                ],
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                ],
                [
                    0.451820102412816, 0.013710451058618,
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                ],
                [
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                ],
                [
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                ],
                [
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                ],
                [
                    0.109575547548147, 0.0146402193249524,
                    0.863012752765897, 0.0127714803610037,
                ],
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                ],
                [
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                ],
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                ],
                [
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                ],
                [
                    0.608123092139794, 0.0113254032838463,
                    0.296091788088397, 0.0844597164879624,
                ],
                [
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        self.points = bary[:, 1:]
        return
